Chapter 13 - Section 13.3 - Solving Nonlinear Systems of Equations - Exercise Set - Page 948: 7

$ x = -\sqrt5, y =-2 $ $ x = -\sqrt5, y = 2$ $x = \sqrt5 , y = -2$ $x = \sqrt5 , y = 2$

1. Divide by 4 $ 16x^{2} - 4y^{2}=64$ $ 4x^{2}- y^{2}= 16 $ 2. Add the two equations $ x^{2}+y^{2}=9$ + $ 4x^{2}- y^{2}= 16 $ $ 5x^{2}= 25 $ $ x^{2}=5 $ $ x= \sqrt 5$ $ x= -\sqrt 5 $ 3. Substitute x $ (\sqrt 5)^{2}+y^{2}=9$ $ y^{2}=4$ $ y=2 , y=-2 $ $ (-\sqrt 5)^{2}+y^{2}=9$ $ y^{2}=4$ $ y=2 , y=-2 $